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Stuck on Level 2

Hey guys (and girls),

I'm posting this because I have hit a road block and I have no idea how to proceed. I've been doing problems on Brilliant for a few months now and don't seem to be making much progress. In fact, over the past month or so I've fallen into a pattern so predictable it's almost like clockwork:

I'll solve the first 2 questions for each topic (Algebra, Number Theory, Combinatorics) very easily. Sometimes even in a matter of seconds. Then, problems 3 and 4 will completely stump me. Then when I give up and go to check the solution, it often turns out I wasn't even on the right track. It's REALLY frustrating.

Anyone have any ideas about how to get past this?

I'm not sure that just "doing more problems" is going to help much on its own, since I've been stuck on the same level for three months already.

Comments

I overcame a similar issue. The issue here is not that you can't do these problems, it's that you aren't learning from the solutions effectively.

My old maths teacher taught us to write a sixty second reflection on the question we just did, answering questions like:
Which techniques did I try?
Did I draw diagrams, were they helpful?
What worked and what didn't work?
What roadblocks did I find?
If I knew/could prove to solve this small part, then how would I solve the rest of the problem?

I'm sure you can think of other examples.

Secondly, there's the skill of how to learn from other's solutions.

Instead of saying "Damn, I wasn't even close" try to reconstruct their argument in your head. If they used a technique you haven't seen before, Google it. When you have finished reading, you should have a feeling that if you saw a similar question on Brilliant next week, you could solve it.

If you post a link to a specific problem, I can show you a worked example of how to interpret the solution.
Good luck.

1) Come back every week! From your profile, I see that you come back and work on problems approximately once a month. It is very hard to improve without consistent effort.

2) Practice practice practice! Use our practice section. Find out which skill you do not know, and then learn about it. It was created to help you acquire the skills needed to reach level 3, so make full use of it.

3) Use the Techniques Trainer! Read the first few articles in each section, till you are fully comfortable with it and understand all the Worked Examples. Note that the difficulty in the examples scales up quickly, so it might take you several read-throughs in order to comprehend the final example.

4) Make comments in solutions! Ask questions like "Can you explain the motivation behind this approach?", "Can you explain this technique?". Even if the original poster doesn't get back to you, there are a lot of other Brilliant members who would love to hop in and explain stuff. In fact, this week's post will be mostly taken from Alexander's explanation in a solution discussions comment.

5) Start discussions! I see you already did :) Keep it up!

6) Review your approaches! Even if you were stuck, is it possible to push through your approach having seen the other solutions? Yes, it might seem brute-force compared to the other nicely presented solutions, but we have to start somewhere. There is (often) more than 1 way to approach a problem.

To me, the skill of learning from others' solutions is probably the most important skill to learn in order to progress in math. Any successful student needs to learn to work smarter, not necessarily harder, and to derive as much learning as possible from each problem.

Wow. I was seriously not expecting such detailed and thoughtful feedback. Thank you everyone for your input.

I can definitely see that I don't spend nearly enough time going over past solutions. I tend to give up far too quickly when I am confronted with a concept that I don't immediately recognise or understand.

Also, I have already been working to fill the gaps in my knowledge of "the basics". Trouble is I'm mostly using Khanacademy, which, while great at teaching core concepts and techniques, doesn't really show how these same basic concepts may be used to solve higher-level problems. Guess it's time to invest in a few Art of Problem Solving books ;-)

How do you know you are not getting better? It could happen tomorrow that all the lights turn on. If not, keep trying. Hopefully, you will develop a deep appreciation for mathematics. That will sustain you. Peaking? That happens to everybody sooner or later.

Hi, Richard. I think one of the possible problems is that you lack the needed backround in Algebra, Number Theory, and Combinatorics. Try to get several textbooks (choose the best), and then do the following. Carefully read the section theory which is explained by the author. Take notes. After that, attempt to solve examples explained by the author before looking at the author's solution. So you should solve them on your own and then check against textbook's solutions. After that, try to solve section problems. Ideally, you should solve at least all the hardest problems. You will work your way through entire textbook, section by section. After you're done with your textbook, begin working with more advanced one. The level of textbook you start with depends on your current level. I assure you that this will help. Good luck!